Search results for: degeneracy

Authors: Yongxu Fu, Shaolong Wan

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We study the band degeneracy, defectiveness, as well as exceptional points of non-Hermitian systems and materials analytically. We elaborate on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions based on developing a general theory of one-dimensional (1D) non-Hermitian systems. We research the presence of the exceptional points in a generalized non-Hermitian Su-Schrieffer-Heeger model under open boundary conditions. Beyond our general theory, there exist infernal points in 1D non-Hermitian systems, where the energy spectra under open boundary conditions converge on some discrete energy values. We study two 1D non-Hermitian models with the existence of infernal points. We generalize the infernal points to the infernal knots in four-dimensional non-Hermitian systems.

Keywords: non-hermitian, degeneracy, defectiveness, exceptional points, infernal points

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Authors: Rachid Fermous, Rima Mebrek

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Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamic multi-fluid equations, we investigated the expansion of dense plasma. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. It is shown that dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.

Keywords: plasma expansion, quantum degeneracy, weakly relativistic, under-dense plasma

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Jatindranath Gain, Madhumita DasSarkar, Sudakshina Kundu

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Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. Topological quantum computation is concerned with two-dimensional many body systems that support excitations. Anyons are elementary building block of quantum computations. When anyons tunneling in a double-layer system can transition to an exotic non-Abelian state and produce Fibonacci anyons, which are powerful enough for universal topological quantum computation (TQC).Here the exotic behavior of Fibonacci Superlattice is studied by using analytical transfer matrix methods and hence Fibonacci anyons. This Fibonacci anyons can build a quantum computer which is very emerging and exciting field today’s in Nanophotonics and quantum computation.

Keywords: quantum computing, quasicrystals, Multiple Quantum wells (MQWs), transfer matrix method, fibonacci anyons, quantum hall effect, nanophotonics

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Authors: Ouardi Okkacha, Kaarour Abedlkrim, Meskine Mohamed

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The effective Hamiltonians are widely used in molecular spectroscopy for the interpretation of the vibration-rotation spectra. Their construction is an ambiguous procedure due to the existence of unitary transformations that change the effective Hamiltonian but do not change its eigenvalues. As a consequence of this ambiguity, it may happen that some parameters of effective Hamiltonians cannot be recovered from experimental data in a unique way. The type of admissible transformations which keeps the operator form of the effective Hamiltonian unaltered and the number of empirically determinable parameters strongly depend on the symmetry type of a molecule (asymmetric top, spherical top, and so on) and on the degeneracy of the vibrational state. In this work, we report the study of the ambiguity of effective Hamiltonian for the fundamental degenerate states v3 of the Molecule 12CD4.

Keywords: 12CD4, high-resolution infrared spectra, tetrahedral tensorial formalism, vibrational states, rovibrational line position analysis, XTDS, SPVIEW

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Kaori Mori Want

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American society is a racially diverse society and there are children books that tell the importance of respecting racial differences. Through reading books, children understand the world around them little by little along with their direct interaction with the world in reality. They find role models in books, strive to be like role models, and grow confidence in who they are. Books thus nurture the mind of children. On the other hand, because of their small presence, children books for multiracial Asian American children are scarce. Multiracial Asian American population is increasing but they are still minority in number. The lack of children’s books for these children may deprive the opportunities of them to embrace their multiraciality positively because they cannot find someone like them in any books. Children books for multiracial Asian American are still not that many, but a few have been being published recently. This paper introduces children books for multiracial Asian American children, and examines how they address issues pertaining to these children, and how they could nurture their self-esteem. Many states of the US used to ban interracial marriages and interracial families and their children once were discriminated against in American society. There was even a theory called the hybrid degeneracy theory which claimed that mixed race children were inferior mentally and physically. In this negative social environment, some multiracial Asian American people report that they had trouble embracing their multiracial identity positively. Yet, children books for these children are full of positive messages. This paper will argue the importance of children books for the mental growth of multiracial Asian American children, and how these books can contribute to the development of multiculturalism in the US in general.

Keywords: critical mixed race studies in the US, hapa children literature, interracial marriage, multiraciality

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Authors: Santanu Pakhira, Chandan Mazumdar, R. Ranganathan, Maxim Avdeev

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Magnetically frustrated systems are of great interest and one of the most adorable topics for the researcher of condensed matter physics, due to their various interesting properties, viz. ground state degeneracy, finite entropy at zero temperature, lowering of ordering temperature, etc. Ternary intermetallics with the composition RE₂TX₃ (RE = rare-earth element, T= d electron transition metal and X= p electron element) crystallize in hexagonal AlB₂ type crystal structure (space group P6/mmm). In a hexagonal crystal structure with the antiferromagnetic interaction between the moments, the center moment is geometrically frustrated. Magnetic frustration along with disorder arrangements of non-magnetic ions are the building blocks for metastable spin-glass ground state formation for most of the compounds of this stoichiometry. The newly synthesized compound Er₂NiSi₃ compound forms in single phase in AlB₂ type structure with space group P6/mmm. The compound orders antiferromagnetically below 5.4 K and spin freezing of the frustrated magnetic moments occurs below 3 K for the compound. The compound shows magnetic relaxation behavior and magnetic memory effect below its freezing temperature. Neutron diffraction patterns for temperatures below the spin freezing temperature have been analyzed using FULLPROF software package. Diffuse magnetic scattering at low temperatures yields spin glass state formation for the compound.

Keywords: antiferromagnetism, magnetic frustration, spin-glass, neutron diffraction

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Authors: Gayatri Ghosh

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In this work, a flavour theory of a neutrino mass model based on A_4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A_4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z_2 × Z_2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δ_CP phase, the neutrino oscillation probability P(νµ → νe), the effective Majorana mass |mee| and |meff νe |. A Z_2 × Z_2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ_13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δ_CP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A_4 × Z_2 × Z_2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalization group effects or by a soft breaking of the A_4 symmetry. In this context the implications for charged lepton flavour violation processes like µ → eγ, τ → eγ, τ → µγ are discussed.

Keywords: Z2 × Z2 invariant perturbations, CLFV, delta CP phase, tribimaximal neutrino mixing

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: Manasa Kalla, Narasimha Raju Chebrolu, Ashok Chatterjee

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We have studied the quantum transport properties of a single molecular transistor in the presence of an external magnetic field using the Keldysh Green function technique. We also used the Anderson-Holstein-Caldeira-Leggett Model to describe the single molecular transistor that consists of a molecular quantum dot (QD) coupled to two metallic leads and placed on a substrate that acts as a heat bath. The phonons are eliminated by the Lang-Firsov transformation and the effective Hamiltonian is used to study the effect of an external magnetic field on the spectral density function, Tunneling Current, Differential Conductance and Spin polarization. A peak in the spectral function corresponds to a possible excitation. In the presence of a magnetic field, the spin-up and spin-down states are degenerate and this degeneracy is lifted by the magnetic field leading to the splitting of the central peak of the spectral function. The tunneling current decreases with increasing magnetic field. We have observed that even the differential conductance peak in the zero magnetic field curve is split in the presence electron-phonon interaction. As the magnetic field is increased, each peak splits into two peaks. And each peak indicates the existence of an energy level. Thus the number of energy levels for transport in the bias window increases with the magnetic field. In the presence of the electron-phonon interaction, Differential Conductance in general gets reduced and decreases faster with the magnetic field. As magnetic field strength increases, the spin polarization of the current is increasing. Our results show that a strongly interacting QD coupled to metallic leads in the presence of external magnetic field parallel to the plane of QD acts as a spin filter at zero temperature.

Keywords: Anderson-Holstein model, Caldeira-Leggett model, spin-polarization, quantum dots

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Authors: Rajlekha Sil

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This paper aims to investigate Ray’s portrayal of liminality and the female gaze in ‘Charulata’ (1964) and ‘Ghare Baire’ (1984), both of which primarily articulates the stories of two women (Charu and Bimala respectively), entangled within the cobwebs of their seething, unfulfilled sexuality, amidst a newly-globalised urban culture, punctuated with political turmoils and ideological conflicts. Their tempestuous interactions with the societal space, both tangible and intangible, that surrounds them, and the men in their lives makes them dwell in a liminal space, filled with an ambiguous sense of virtue. In Ray’s films, this sexual ambivalence is characterised by the liminality between the scenic and extrascenic spaces, which, in turn, defines the female gaze as the director’s lenses paint a picture of the new wave of socio-political and socio-cultural movements in early twentieth-century Bengal. Brinda Bose’s essay on ‘Modernity, Globality, Sexuality, and the City: A Reading of Indian Cinema’, analyses the ‘necessary’ process of urbanisation as a marker of ‘moral degeneracy of the nation easily analogous with female sexual transgression/ promiscuity with the nation personified as a woman, by using the concept of the liminal space, a site of both empowerment through transgression and containment through regulation.’ My paper, however, would focus on the liminal space propagated by Ray through his contrasting depiction of scenic and extrascenic spaces to satiate the equivocal voices in Charu and Bimala, along with their way of ‘gazing’ into an equally disheveled society - a gaze that helps them transcend the barriers of politics and urbanization into a state of universal uniformity, symmetrical with their sexual immorality. The first section of the paper would explore Ray’s usage of these theatrical spaces through his character sketches, shots and dialogues, while the second section of the paper would delve into the ‘female gaze’ on a newly revolutionised society.

Keywords: satyajit ray, space, gaze, female sexuality, charulata, ghare baire

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Authors: Inbal Zuriely, Yonit Weiss, Hilla Zaharoni, Hadas Lewkowicz, Tatiana Vander, Tarif Bader

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early active movement, along with adjusting optimal nutrition, prevents aggravation of muscle degeneracy and functional decline. Eating is a basic activity of daily life, which reflects the patient's independence. When eating and feeding are experienced successfully, they lead to a sense of pleasure and satisfaction. However, when they are experienced as a difficulty, they might evoke feelings of helplessness and frustration. This stresses the essential process of gradual weaning off the enteral feeding tube. the work describes the collaboration of a dietitian, determining the nutritional needs of patients undergoing enteral tube weaning as part of the rehabilitation process, with the suited treatment of an occupational therapist. Occupational therapy intervention regarding eating capabilities focuses on improving the required motor and cognitive components, along with environmental adjustments and aids, imparting eating strategies and training to patients and their families. The project was conducted in the long-term, ventilated patients’ department at the Herzfeld Rehabilitation Geriatric Medical Center on patients undergoing enteral tube weaning with the staff’s assistance. Establishing continuous collaboration between the dietician and the occupational therapist, starting from the beginning of the feeding-tube weaning process: 1.The dietician updates the occupational therapist about the start of the process and the approved diet. 2.The occupational therapist performs cognitive, motor, and functional assessments and treatments regarding the patient’s eating capabilities and recommends the required adjustments for independent eating according to the FIM (Functional Independence Measure) scale. 3.The occupational therapist closely follows up on the patient’s degree of independence in eating and provides a repeated update to the dietician. 4.The dietician accordingly guides the ward staff on whether and how to feed the patient or allow independent eating. The project aimed to promote patients toward independent feeding, which leads to a sense of empowerment, enjoyment of the eating experience, and progress of functional ability, along with performing active movements that will motivate mobilization. From the beginning of 2022, 26 patients participated in the project. 79% of all patients who started the weaning process from tube feeding achieved different levels of independence in feeding (independence levels ranged from supervision (FIM-5) to complete independence (FIM-7). The integration of occupational therapy and dietary treatment is based on a patient-centered approach while considering the patient’s personal needs, preferences, and goals. This interdisciplinary partnership is essential for meeting the complex needs of prolonged mechanically ventilated patients and promotes independent functioning and quality of life.

Keywords: dietary, mechanical ventilation, occupational therapy, tube feeding weaning

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Authors: Moustafa Osman Mohammed

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This paper introduces topological order in descried social systems starting with the original concept of autopoiesis by biologists and scientists, including the modification of general systems based on socialized medicine. Topological order is important in describing the physical systems for exploiting optical systems and improving photonic devices. The stats of topological order have some interesting properties of topological degeneracy and fractional statistics that reveal the entanglement origin of topological order, etc. Topological ideas in photonics form exciting developments in solid-state materials, that being; insulating in the bulk, conducting electricity on their surface without dissipation or back-scattering, even in the presence of large impurities. A specific type of autopoiesis system is interrelated to the main categories amongst existing groups of the ecological phenomena interaction social and medical sciences. The hypothesis, nevertheless, has a nonlinear interaction with its natural environment 'interactional cycle' for exchange photon energy with molecules without changes in topology. The engineering topology of a biosensor is based on the excitation boundary of surface electromagnetic waves in photonic band gap multilayer films. The device operation is similar to surface Plasmonic biosensors in which a photonic band gap film replaces metal film as the medium when surface electromagnetic waves are excited. The use of photonic band gap film offers sharper surface wave resonance leading to the potential of greatly enhanced sensitivity. So, the properties of the photonic band gap material are engineered to operate a sensor at any wavelength and conduct a surface wave resonance that ranges up to 470 nm. The wavelength is not generally accessible with surface Plasmon sensing. Lastly, the photonic band gap films have robust mechanical functions that offer new substrates for surface chemistry to understand the molecular design structure and create sensing chips surface with different concentrations of DNA sequences in the solution to observe and track the surface mode resonance under the influences of processes that take place in the spectroscopic environment. These processes led to the development of several advanced analytical technologies: which are; automated, real-time, reliable, reproducible, and cost-effective. This results in faster and more accurate monitoring and detection of biomolecules on refractive index sensing, antibody-antigen reactions with a DNA or protein binding. Ultimately, the controversial aspect of molecular frictional properties is adjusted to each other in order to form unique spatial structure and dynamics of biological molecules for providing the environment mutual contribution in investigation of changes due to the pathogenic archival architecture of cell clusters.

Keywords: autopoiesis, photonics systems, quantum topology, molecular structure, biosensing

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